Properties

Label 177.5.b.a.119.9
Level $177$
Weight $5$
Character 177.119
Analytic conductor $18.296$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(78\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.9
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.70

$q$-expansion

\(f(q)\) \(=\) \(q-6.47467i q^{2} +(-8.82514 - 1.76549i) q^{3} -25.9214 q^{4} +26.7513i q^{5} +(-11.4310 + 57.1399i) q^{6} -48.5383 q^{7} +64.2378i q^{8} +(74.7661 + 31.1614i) q^{9} +O(q^{10})\) \(q-6.47467i q^{2} +(-8.82514 - 1.76549i) q^{3} -25.9214 q^{4} +26.7513i q^{5} +(-11.4310 + 57.1399i) q^{6} -48.5383 q^{7} +64.2378i q^{8} +(74.7661 + 31.1614i) q^{9} +173.206 q^{10} +66.3235i q^{11} +(228.760 + 45.7639i) q^{12} -17.1474 q^{13} +314.270i q^{14} +(47.2291 - 236.084i) q^{15} +1.17649 q^{16} -329.024i q^{17} +(201.760 - 484.086i) q^{18} +308.577 q^{19} -693.430i q^{20} +(428.357 + 85.6938i) q^{21} +429.423 q^{22} -68.4764i q^{23} +(113.411 - 566.908i) q^{24} -90.6302 q^{25} +111.024i q^{26} +(-604.806 - 407.002i) q^{27} +1258.18 q^{28} +178.384i q^{29} +(-1528.56 - 305.793i) q^{30} +80.5949 q^{31} +1020.19i q^{32} +(117.093 - 585.314i) q^{33} -2130.32 q^{34} -1298.46i q^{35} +(-1938.04 - 807.746i) q^{36} +1120.58 q^{37} -1997.94i q^{38} +(151.328 + 30.2735i) q^{39} -1718.44 q^{40} +426.250i q^{41} +(554.840 - 2773.47i) q^{42} +1032.93 q^{43} -1719.20i q^{44} +(-833.606 + 2000.09i) q^{45} -443.362 q^{46} -574.063i q^{47} +(-10.3827 - 2.07709i) q^{48} -45.0329 q^{49} +586.801i q^{50} +(-580.888 + 2903.68i) q^{51} +444.484 q^{52} +409.120i q^{53} +(-2635.21 + 3915.92i) q^{54} -1774.24 q^{55} -3117.99i q^{56} +(-2723.24 - 544.790i) q^{57} +1154.98 q^{58} -453.188i q^{59} +(-1224.24 + 6119.62i) q^{60} +4085.24 q^{61} -521.826i q^{62} +(-3629.02 - 1512.52i) q^{63} +6624.21 q^{64} -458.714i q^{65} +(-3789.72 - 758.141i) q^{66} +8024.54 q^{67} +8528.76i q^{68} +(-120.894 + 604.313i) q^{69} -8407.11 q^{70} -9533.81i q^{71} +(-2001.74 + 4802.81i) q^{72} +6393.64 q^{73} -7255.40i q^{74} +(799.824 + 160.007i) q^{75} -7998.76 q^{76} -3219.23i q^{77} +(196.011 - 979.799i) q^{78} -2585.51 q^{79} +31.4727i q^{80} +(4618.94 + 4659.63i) q^{81} +2759.83 q^{82} -3769.55i q^{83} +(-11103.6 - 2221.30i) q^{84} +8801.80 q^{85} -6687.86i q^{86} +(314.936 - 1574.27i) q^{87} -4260.48 q^{88} +5967.21i q^{89} +(12949.9 + 5397.33i) q^{90} +832.305 q^{91} +1775.00i q^{92} +(-711.261 - 142.289i) q^{93} -3716.87 q^{94} +8254.84i q^{95} +(1801.13 - 9003.30i) q^{96} +15383.8 q^{97} +291.573i q^{98} +(-2066.73 + 4958.75i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} + O(q^{10}) \) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} - 156q^{10} - 4q^{13} + 13q^{15} + 4948q^{16} + 22q^{18} + 812q^{19} - 173q^{21} - 1644q^{22} - 678q^{24} - 8238q^{25} + 777q^{27} - 3764q^{28} + 1374q^{30} + 4664q^{31} - 1042q^{33} + 3244q^{34} + 3648q^{36} - 3960q^{37} - 7078q^{39} - 1576q^{40} + 4934q^{42} - 1492q^{43} - 2063q^{45} - 2036q^{46} - 2620q^{48} + 24274q^{49} + 7300q^{51} + 8408q^{52} - 14766q^{54} + 9780q^{55} + 6939q^{57} - 3856q^{58} + 4712q^{60} - 212q^{61} - 7438q^{63} - 45760q^{64} + 3048q^{66} - 12972q^{67} + 21672q^{69} + 5828q^{70} - 866q^{72} - 5240q^{73} - 20922q^{75} + 12368q^{76} - 16508q^{78} - 14976q^{79} + 25524q^{81} - 14484q^{82} + 9540q^{84} + 11572q^{85} + 5695q^{87} + 62160q^{88} - 31672q^{90} + 8284q^{91} - 9590q^{93} - 10992q^{94} + 34102q^{96} - 55000q^{97} - 14254q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.47467i 1.61867i −0.587348 0.809334i \(-0.699828\pi\)
0.587348 0.809334i \(-0.300172\pi\)
\(3\) −8.82514 1.76549i −0.980571 0.196165i
\(4\) −25.9214 −1.62009
\(5\) 26.7513i 1.07005i 0.844836 + 0.535025i \(0.179698\pi\)
−0.844836 + 0.535025i \(0.820302\pi\)
\(6\) −11.4310 + 57.1399i −0.317527 + 1.58722i
\(7\) −48.5383 −0.990578 −0.495289 0.868728i \(-0.664938\pi\)
−0.495289 + 0.868728i \(0.664938\pi\)
\(8\) 64.2378i 1.00372i
\(9\) 74.7661 + 31.1614i 0.923038 + 0.384708i
\(10\) 173.206 1.73206
\(11\) 66.3235i 0.548128i 0.961711 + 0.274064i \(0.0883680\pi\)
−0.961711 + 0.274064i \(0.911632\pi\)
\(12\) 228.760 + 45.7639i 1.58861 + 0.317805i
\(13\) −17.1474 −0.101464 −0.0507319 0.998712i \(-0.516155\pi\)
−0.0507319 + 0.998712i \(0.516155\pi\)
\(14\) 314.270i 1.60342i
\(15\) 47.2291 236.084i 0.209907 1.04926i
\(16\) 1.17649 0.00459568
\(17\) 329.024i 1.13849i −0.822168 0.569245i \(-0.807235\pi\)
0.822168 0.569245i \(-0.192765\pi\)
\(18\) 201.760 484.086i 0.622715 1.49409i
\(19\) 308.577 0.854785 0.427393 0.904066i \(-0.359432\pi\)
0.427393 + 0.904066i \(0.359432\pi\)
\(20\) 693.430i 1.73358i
\(21\) 428.357 + 85.6938i 0.971332 + 0.194317i
\(22\) 429.423 0.887237
\(23\) 68.4764i 0.129445i −0.997903 0.0647225i \(-0.979384\pi\)
0.997903 0.0647225i \(-0.0206162\pi\)
\(24\) 113.411 566.908i 0.196894 0.984214i
\(25\) −90.6302 −0.145008
\(26\) 111.024i 0.164236i
\(27\) −604.806 407.002i −0.829638 0.558302i
\(28\) 1258.18 1.60482
\(29\) 178.384i 0.212110i 0.994360 + 0.106055i \(0.0338219\pi\)
−0.994360 + 0.106055i \(0.966178\pi\)
\(30\) −1528.56 305.793i −1.69840 0.339770i
\(31\) 80.5949 0.0838656 0.0419328 0.999120i \(-0.486648\pi\)
0.0419328 + 0.999120i \(0.486648\pi\)
\(32\) 1020.19i 0.996277i
\(33\) 117.093 585.314i 0.107524 0.537478i
\(34\) −2130.32 −1.84284
\(35\) 1298.46i 1.05997i
\(36\) −1938.04 807.746i −1.49540 0.623261i
\(37\) 1120.58 0.818541 0.409270 0.912413i \(-0.365783\pi\)
0.409270 + 0.912413i \(0.365783\pi\)
\(38\) 1997.94i 1.38361i
\(39\) 151.328 + 30.2735i 0.0994924 + 0.0199037i
\(40\) −1718.44 −1.07403
\(41\) 426.250i 0.253569i 0.991930 + 0.126785i \(0.0404657\pi\)
−0.991930 + 0.126785i \(0.959534\pi\)
\(42\) 554.840 2773.47i 0.314535 1.57226i
\(43\) 1032.93 0.558640 0.279320 0.960198i \(-0.409891\pi\)
0.279320 + 0.960198i \(0.409891\pi\)
\(44\) 1719.20i 0.888015i
\(45\) −833.606 + 2000.09i −0.411657 + 0.987698i
\(46\) −443.362 −0.209528
\(47\) 574.063i 0.259874i −0.991522 0.129937i \(-0.958522\pi\)
0.991522 0.129937i \(-0.0414776\pi\)
\(48\) −10.3827 2.07709i −0.00450639 0.000901513i
\(49\) −45.0329 −0.0187559
\(50\) 586.801i 0.234720i
\(51\) −580.888 + 2903.68i −0.223332 + 1.11637i
\(52\) 444.484 0.164380
\(53\) 409.120i 0.145646i 0.997345 + 0.0728230i \(0.0232008\pi\)
−0.997345 + 0.0728230i \(0.976799\pi\)
\(54\) −2635.21 + 3915.92i −0.903706 + 1.34291i
\(55\) −1774.24 −0.586525
\(56\) 3117.99i 0.994258i
\(57\) −2723.24 544.790i −0.838177 0.167679i
\(58\) 1154.98 0.343335
\(59\) 453.188i 0.130189i
\(60\) −1224.24 + 6119.62i −0.340068 + 1.69989i
\(61\) 4085.24 1.09789 0.548944 0.835859i \(-0.315030\pi\)
0.548944 + 0.835859i \(0.315030\pi\)
\(62\) 521.826i 0.135751i
\(63\) −3629.02 1512.52i −0.914341 0.381083i
\(64\) 6624.21 1.61724
\(65\) 458.714i 0.108571i
\(66\) −3789.72 758.141i −0.869999 0.174045i
\(67\) 8024.54 1.78760 0.893800 0.448466i \(-0.148029\pi\)
0.893800 + 0.448466i \(0.148029\pi\)
\(68\) 8528.76i 1.84445i
\(69\) −120.894 + 604.313i −0.0253926 + 0.126930i
\(70\) −8407.11 −1.71574
\(71\) 9533.81i 1.89125i −0.325254 0.945627i \(-0.605450\pi\)
0.325254 0.945627i \(-0.394550\pi\)
\(72\) −2001.74 + 4802.81i −0.386138 + 0.926468i
\(73\) 6393.64 1.19978 0.599891 0.800082i \(-0.295211\pi\)
0.599891 + 0.800082i \(0.295211\pi\)
\(74\) 7255.40i 1.32495i
\(75\) 799.824 + 160.007i 0.142191 + 0.0284456i
\(76\) −7998.76 −1.38483
\(77\) 3219.23i 0.542963i
\(78\) 196.011 979.799i 0.0322175 0.161045i
\(79\) −2585.51 −0.414278 −0.207139 0.978312i \(-0.566415\pi\)
−0.207139 + 0.978312i \(0.566415\pi\)
\(80\) 31.4727i 0.00491761i
\(81\) 4618.94 + 4659.63i 0.703999 + 0.710201i
\(82\) 2759.83 0.410444
\(83\) 3769.55i 0.547183i −0.961846 0.273592i \(-0.911788\pi\)
0.961846 0.273592i \(-0.0882117\pi\)
\(84\) −11103.6 2221.30i −1.57364 0.314811i
\(85\) 8801.80 1.21824
\(86\) 6687.86i 0.904254i
\(87\) 314.936 1574.27i 0.0416086 0.207989i
\(88\) −4260.48 −0.550165
\(89\) 5967.21i 0.753340i 0.926347 + 0.376670i \(0.122931\pi\)
−0.926347 + 0.376670i \(0.877069\pi\)
\(90\) 12949.9 + 5397.33i 1.59875 + 0.666337i
\(91\) 832.305 0.100508
\(92\) 1775.00i 0.209712i
\(93\) −711.261 142.289i −0.0822362 0.0164515i
\(94\) −3716.87 −0.420651
\(95\) 8254.84i 0.914663i
\(96\) 1801.13 9003.30i 0.195435 0.976920i
\(97\) 15383.8 1.63501 0.817503 0.575925i \(-0.195358\pi\)
0.817503 + 0.575925i \(0.195358\pi\)
\(98\) 291.573i 0.0303595i
\(99\) −2066.73 + 4958.75i −0.210869 + 0.505943i
\(100\) 2349.26 0.234926
\(101\) 10477.0i 1.02706i 0.858072 + 0.513530i \(0.171663\pi\)
−0.858072 + 0.513530i \(0.828337\pi\)
\(102\) 18800.4 + 3761.06i 1.80703 + 0.361501i
\(103\) 2261.28 0.213148 0.106574 0.994305i \(-0.466012\pi\)
0.106574 + 0.994305i \(0.466012\pi\)
\(104\) 1101.51i 0.101841i
\(105\) −2292.42 + 11459.1i −0.207929 + 1.03937i
\(106\) 2648.92 0.235753
\(107\) 21108.2i 1.84368i −0.387576 0.921838i \(-0.626688\pi\)
0.387576 0.921838i \(-0.373312\pi\)
\(108\) 15677.4 + 10550.1i 1.34409 + 0.904498i
\(109\) 5238.41 0.440906 0.220453 0.975398i \(-0.429246\pi\)
0.220453 + 0.975398i \(0.429246\pi\)
\(110\) 11487.6i 0.949389i
\(111\) −9889.29 1978.38i −0.802637 0.160569i
\(112\) −57.1050 −0.00455237
\(113\) 10631.5i 0.832605i 0.909226 + 0.416302i \(0.136674\pi\)
−0.909226 + 0.416302i \(0.863326\pi\)
\(114\) −3527.34 + 17632.1i −0.271417 + 1.35673i
\(115\) 1831.83 0.138513
\(116\) 4623.97i 0.343636i
\(117\) −1282.04 534.336i −0.0936549 0.0390339i
\(118\) −2934.24 −0.210733
\(119\) 15970.3i 1.12776i
\(120\) 15165.5 + 3033.89i 1.05316 + 0.210687i
\(121\) 10242.2 0.699556
\(122\) 26450.6i 1.77712i
\(123\) 752.539 3761.71i 0.0497415 0.248642i
\(124\) −2089.13 −0.135870
\(125\) 14295.1i 0.914884i
\(126\) −9793.07 + 23496.7i −0.616848 + 1.48001i
\(127\) −24055.7 −1.49145 −0.745727 0.666252i \(-0.767898\pi\)
−0.745727 + 0.666252i \(0.767898\pi\)
\(128\) 26566.6i 1.62149i
\(129\) −9115.71 1823.62i −0.547786 0.109586i
\(130\) −2970.02 −0.175741
\(131\) 19555.5i 1.13953i 0.821807 + 0.569767i \(0.192966\pi\)
−0.821807 + 0.569767i \(0.807034\pi\)
\(132\) −3035.22 + 15172.2i −0.174198 + 0.870762i
\(133\) −14977.8 −0.846731
\(134\) 51956.3i 2.89353i
\(135\) 10887.8 16179.3i 0.597411 0.887755i
\(136\) 21135.8 1.14272
\(137\) 10205.1i 0.543720i 0.962337 + 0.271860i \(0.0876388\pi\)
−0.962337 + 0.271860i \(0.912361\pi\)
\(138\) 3912.73 + 782.751i 0.205457 + 0.0411022i
\(139\) −20686.8 −1.07069 −0.535344 0.844634i \(-0.679818\pi\)
−0.535344 + 0.844634i \(0.679818\pi\)
\(140\) 33657.9i 1.71724i
\(141\) −1013.50 + 5066.18i −0.0509784 + 0.254825i
\(142\) −61728.3 −3.06131
\(143\) 1137.27i 0.0556151i
\(144\) 87.9618 + 36.6611i 0.00424198 + 0.00176799i
\(145\) −4772.01 −0.226968
\(146\) 41396.7i 1.94205i
\(147\) 397.421 + 79.5050i 0.0183915 + 0.00367925i
\(148\) −29047.1 −1.32611
\(149\) 30863.4i 1.39018i 0.718923 + 0.695090i \(0.244635\pi\)
−0.718923 + 0.695090i \(0.755365\pi\)
\(150\) 1035.99 5178.60i 0.0460440 0.230160i
\(151\) 20970.3 0.919709 0.459854 0.887994i \(-0.347902\pi\)
0.459854 + 0.887994i \(0.347902\pi\)
\(152\) 19822.3i 0.857961i
\(153\) 10252.8 24599.8i 0.437987 1.05087i
\(154\) −20843.5 −0.878878
\(155\) 2156.01i 0.0897405i
\(156\) −3922.63 784.732i −0.161186 0.0322457i
\(157\) 38969.6 1.58098 0.790490 0.612475i \(-0.209826\pi\)
0.790490 + 0.612475i \(0.209826\pi\)
\(158\) 16740.3i 0.670578i
\(159\) 722.297 3610.54i 0.0285707 0.142816i
\(160\) −27291.3 −1.06607
\(161\) 3323.73i 0.128225i
\(162\) 30169.6 29906.1i 1.14958 1.13954i
\(163\) −29092.1 −1.09496 −0.547482 0.836818i \(-0.684413\pi\)
−0.547482 + 0.836818i \(0.684413\pi\)
\(164\) 11049.0i 0.410804i
\(165\) 15657.9 + 3132.40i 0.575129 + 0.115056i
\(166\) −24406.6 −0.885709
\(167\) 30094.7i 1.07909i 0.841957 + 0.539545i \(0.181404\pi\)
−0.841957 + 0.539545i \(0.818596\pi\)
\(168\) −5504.79 + 27516.7i −0.195039 + 0.974941i
\(169\) −28267.0 −0.989705
\(170\) 56988.8i 1.97193i
\(171\) 23071.1 + 9615.70i 0.788999 + 0.328843i
\(172\) −26774.9 −0.905046
\(173\) 31591.9i 1.05556i −0.849381 0.527781i \(-0.823024\pi\)
0.849381 0.527781i \(-0.176976\pi\)
\(174\) −10192.9 2039.10i −0.336665 0.0673505i
\(175\) 4399.04 0.143642
\(176\) 78.0291i 0.00251902i
\(177\) −800.098 + 3999.44i −0.0255386 + 0.127659i
\(178\) 38635.7 1.21941
\(179\) 7027.75i 0.219336i −0.993968 0.109668i \(-0.965021\pi\)
0.993968 0.109668i \(-0.0349788\pi\)
\(180\) 21608.2 51845.1i 0.666921 1.60016i
\(181\) 50951.9 1.55526 0.777631 0.628721i \(-0.216421\pi\)
0.777631 + 0.628721i \(0.216421\pi\)
\(182\) 5388.90i 0.162689i
\(183\) −36052.8 7212.44i −1.07656 0.215368i
\(184\) 4398.77 0.129926
\(185\) 29977.0i 0.875880i
\(186\) −921.277 + 4605.18i −0.0266296 + 0.133113i
\(187\) 21822.0 0.624038
\(188\) 14880.5i 0.421019i
\(189\) 29356.3 + 19755.2i 0.821821 + 0.553041i
\(190\) 53447.4 1.48054
\(191\) 36553.1i 1.00198i 0.865454 + 0.500988i \(0.167030\pi\)
−0.865454 + 0.500988i \(0.832970\pi\)
\(192\) −58459.5 11695.0i −1.58582 0.317246i
\(193\) −34412.9 −0.923862 −0.461931 0.886916i \(-0.652843\pi\)
−0.461931 + 0.886916i \(0.652843\pi\)
\(194\) 99604.9i 2.64653i
\(195\) −809.855 + 4048.21i −0.0212980 + 0.106462i
\(196\) 1167.31 0.0303862
\(197\) 20824.8i 0.536597i −0.963336 0.268298i \(-0.913539\pi\)
0.963336 0.268298i \(-0.0864613\pi\)
\(198\) 32106.3 + 13381.4i 0.818954 + 0.341328i
\(199\) −67155.1 −1.69579 −0.847897 0.530161i \(-0.822131\pi\)
−0.847897 + 0.530161i \(0.822131\pi\)
\(200\) 5821.88i 0.145547i
\(201\) −70817.6 14167.2i −1.75287 0.350665i
\(202\) 67835.4 1.66247
\(203\) 8658.47i 0.210111i
\(204\) 15057.4 75267.4i 0.361818 1.80862i
\(205\) −11402.7 −0.271332
\(206\) 14641.1i 0.345015i
\(207\) 2133.82 5119.71i 0.0497985 0.119483i
\(208\) −20.1738 −0.000466295
\(209\) 20465.9i 0.468532i
\(210\) 74193.9 + 14842.7i 1.68240 + 0.336568i
\(211\) 63630.6 1.42923 0.714613 0.699520i \(-0.246603\pi\)
0.714613 + 0.699520i \(0.246603\pi\)
\(212\) 10605.0i 0.235959i
\(213\) −16831.8 + 84137.2i −0.370999 + 1.85451i
\(214\) −136669. −2.98430
\(215\) 27632.1i 0.597773i
\(216\) 26144.9 38851.4i 0.560376 0.832721i
\(217\) −3911.94 −0.0830754
\(218\) 33917.0i 0.713681i
\(219\) −56424.7 11287.9i −1.17647 0.235356i
\(220\) 45990.7 0.950221
\(221\) 5641.89i 0.115516i
\(222\) −12809.3 + 64029.9i −0.259909 + 1.29920i
\(223\) 60412.0 1.21482 0.607412 0.794387i \(-0.292208\pi\)
0.607412 + 0.794387i \(0.292208\pi\)
\(224\) 49518.2i 0.986890i
\(225\) −6776.06 2824.16i −0.133848 0.0557859i
\(226\) 68835.7 1.34771
\(227\) 45524.1i 0.883466i −0.897147 0.441733i \(-0.854364\pi\)
0.897147 0.441733i \(-0.145636\pi\)
\(228\) 70590.1 + 14121.7i 1.35792 + 0.271655i
\(229\) 19054.3 0.363348 0.181674 0.983359i \(-0.441848\pi\)
0.181674 + 0.983359i \(0.441848\pi\)
\(230\) 11860.5i 0.224206i
\(231\) −5683.51 + 28410.1i −0.106511 + 0.532414i
\(232\) −11459.0 −0.212898
\(233\) 84699.7i 1.56016i −0.625678 0.780081i \(-0.715178\pi\)
0.625678 0.780081i \(-0.284822\pi\)
\(234\) −3459.65 + 8300.81i −0.0631830 + 0.151596i
\(235\) 15356.9 0.278079
\(236\) 11747.3i 0.210917i
\(237\) 22817.5 + 4564.68i 0.406229 + 0.0812670i
\(238\) 103402. 1.82547
\(239\) 102141.i 1.78815i −0.447918 0.894075i \(-0.647834\pi\)
0.447918 0.894075i \(-0.352166\pi\)
\(240\) 55.5647 277.751i 0.000964664 0.00482206i
\(241\) 8557.27 0.147333 0.0736667 0.997283i \(-0.476530\pi\)
0.0736667 + 0.997283i \(0.476530\pi\)
\(242\) 66314.9i 1.13235i
\(243\) −32536.2 49276.5i −0.551004 0.834502i
\(244\) −105895. −1.77867
\(245\) 1204.69i 0.0200697i
\(246\) −24355.9 4872.44i −0.402470 0.0805150i
\(247\) −5291.29 −0.0867297
\(248\) 5177.24i 0.0841773i
\(249\) −6655.09 + 33266.8i −0.107338 + 0.536552i
\(250\) 92555.9 1.48089
\(251\) 43678.6i 0.693300i 0.937995 + 0.346650i \(0.112681\pi\)
−0.937995 + 0.346650i \(0.887319\pi\)
\(252\) 94069.3 + 39206.6i 1.48131 + 0.617388i
\(253\) 4541.59 0.0709524
\(254\) 155753.i 2.41417i
\(255\) −77677.1 15539.5i −1.19457 0.238977i
\(256\) −66022.6 −1.00742
\(257\) 49137.2i 0.743951i −0.928243 0.371976i \(-0.878681\pi\)
0.928243 0.371976i \(-0.121319\pi\)
\(258\) −11807.3 + 59021.3i −0.177383 + 0.886685i
\(259\) −54391.2 −0.810828
\(260\) 11890.5i 0.175895i
\(261\) −5558.70 + 13337.1i −0.0816004 + 0.195785i
\(262\) 126616. 1.84453
\(263\) 102582.i 1.48306i 0.670919 + 0.741531i \(0.265900\pi\)
−0.670919 + 0.741531i \(0.734100\pi\)
\(264\) 37599.3 + 7521.82i 0.539475 + 0.107923i
\(265\) −10944.5 −0.155849
\(266\) 96976.5i 1.37058i
\(267\) 10535.0 52661.4i 0.147779 0.738703i
\(268\) −208007. −2.89607
\(269\) 19982.6i 0.276151i 0.990422 + 0.138076i \(0.0440917\pi\)
−0.990422 + 0.138076i \(0.955908\pi\)
\(270\) −104756. 70495.1i −1.43698 0.967011i
\(271\) 926.550 0.0126162 0.00630812 0.999980i \(-0.497992\pi\)
0.00630812 + 0.999980i \(0.497992\pi\)
\(272\) 387.094i 0.00523213i
\(273\) −7345.20 1469.42i −0.0985550 0.0197161i
\(274\) 66074.6 0.880103
\(275\) 6010.91i 0.0794831i
\(276\) 3133.75 15664.6i 0.0411383 0.205638i
\(277\) −127962. −1.66771 −0.833857 0.551981i \(-0.813872\pi\)
−0.833857 + 0.551981i \(0.813872\pi\)
\(278\) 133940.i 1.73309i
\(279\) 6025.76 + 2511.45i 0.0774112 + 0.0322638i
\(280\) 83410.3 1.06391
\(281\) 77722.8i 0.984319i 0.870505 + 0.492160i \(0.163792\pi\)
−0.870505 + 0.492160i \(0.836208\pi\)
\(282\) 32801.9 + 6562.09i 0.412478 + 0.0825171i
\(283\) 14238.3 0.177781 0.0888907 0.996041i \(-0.471668\pi\)
0.0888907 + 0.996041i \(0.471668\pi\)
\(284\) 247130.i 3.06400i
\(285\) 14573.8 72850.1i 0.179425 0.896892i
\(286\) −7363.48 −0.0900224
\(287\) 20689.4i 0.251180i
\(288\) −31790.4 + 76275.4i −0.383276 + 0.919602i
\(289\) −24735.6 −0.296161
\(290\) 30897.2i 0.367386i
\(291\) −135764. 27159.9i −1.60324 0.320732i
\(292\) −165732. −1.94375
\(293\) 94699.3i 1.10309i 0.834145 + 0.551546i \(0.185962\pi\)
−0.834145 + 0.551546i \(0.814038\pi\)
\(294\) 514.769 2573.17i 0.00595549 0.0297697i
\(295\) 12123.3 0.139309
\(296\) 71983.7i 0.821582i
\(297\) 26993.8 40112.8i 0.306021 0.454748i
\(298\) 199830. 2.25024
\(299\) 1174.19i 0.0131340i
\(300\) −20732.5 4147.59i −0.230362 0.0460844i
\(301\) −50136.5 −0.553377
\(302\) 135776.i 1.48870i
\(303\) 18497.1 92461.3i 0.201474 1.00711i
\(304\) 363.039 0.00392832
\(305\) 109285.i 1.17480i
\(306\) −159276. 66383.7i −1.70101 0.708955i
\(307\) 118694. 1.25937 0.629685 0.776850i \(-0.283184\pi\)
0.629685 + 0.776850i \(0.283184\pi\)
\(308\) 83446.9i 0.879648i
\(309\) −19956.1 3992.27i −0.209006 0.0418122i
\(310\) 13959.5 0.145260
\(311\) 11227.5i 0.116082i −0.998314 0.0580409i \(-0.981515\pi\)
0.998314 0.0580409i \(-0.0184854\pi\)
\(312\) −1944.70 + 9720.98i −0.0199776 + 0.0998621i
\(313\) 43090.7 0.439840 0.219920 0.975518i \(-0.429420\pi\)
0.219920 + 0.975518i \(0.429420\pi\)
\(314\) 252315.i 2.55908i
\(315\) 40461.8 97080.9i 0.407778 0.978391i
\(316\) 67020.0 0.671166
\(317\) 34372.0i 0.342047i −0.985267 0.171024i \(-0.945293\pi\)
0.985267 0.171024i \(-0.0547075\pi\)
\(318\) −23377.1 4676.63i −0.231172 0.0462465i
\(319\) −11831.1 −0.116263
\(320\) 177206.i 1.73053i
\(321\) −37266.4 + 186283.i −0.361665 + 1.80785i
\(322\) 21520.0 0.207554
\(323\) 101529.i 0.973165i
\(324\) −119729. 120784.i −1.14054 1.15059i
\(325\) 1554.07 0.0147131
\(326\) 188362.i 1.77238i
\(327\) −46229.7 9248.35i −0.432340 0.0864906i
\(328\) −27381.3 −0.254511
\(329\) 27864.0i 0.257426i
\(330\) 20281.2 101380.i 0.186237 0.930943i
\(331\) −75885.6 −0.692633 −0.346317 0.938118i \(-0.612568\pi\)
−0.346317 + 0.938118i \(0.612568\pi\)
\(332\) 97711.9i 0.886485i
\(333\) 83781.6 + 34918.9i 0.755544 + 0.314899i
\(334\) 194854. 1.74669
\(335\) 214666.i 1.91282i
\(336\) 503.959 + 100.818i 0.00446392 + 0.000893018i
\(337\) 142500. 1.25474 0.627371 0.778721i \(-0.284131\pi\)
0.627371 + 0.778721i \(0.284131\pi\)
\(338\) 183019.i 1.60200i
\(339\) 18769.9 93824.7i 0.163328 0.816428i
\(340\) −228155. −1.97366
\(341\) 5345.33i 0.0459691i
\(342\) 62258.5 149378.i 0.532288 1.27713i
\(343\) 118726. 1.00916
\(344\) 66352.9i 0.560716i
\(345\) −16166.1 3234.07i −0.135821 0.0271714i
\(346\) −204547. −1.70860
\(347\) 184710.i 1.53402i −0.641635 0.767010i \(-0.721744\pi\)
0.641635 0.767010i \(-0.278256\pi\)
\(348\) −8163.57 + 40807.2i −0.0674096 + 0.336960i
\(349\) −68094.4 −0.559062 −0.279531 0.960137i \(-0.590179\pi\)
−0.279531 + 0.960137i \(0.590179\pi\)
\(350\) 28482.3i 0.232509i
\(351\) 10370.8 + 6979.02i 0.0841782 + 0.0566474i
\(352\) −67662.4 −0.546087
\(353\) 2116.15i 0.0169823i 0.999964 + 0.00849116i \(0.00270285\pi\)
−0.999964 + 0.00849116i \(0.997297\pi\)
\(354\) 25895.1 + 5180.37i 0.206638 + 0.0413385i
\(355\) 255041. 2.02374
\(356\) 154678.i 1.22048i
\(357\) 28195.3 140940.i 0.221228 1.10585i
\(358\) −45502.4 −0.355033
\(359\) 102400.i 0.794532i −0.917704 0.397266i \(-0.869959\pi\)
0.917704 0.397266i \(-0.130041\pi\)
\(360\) −128481. 53549.0i −0.991368 0.413187i
\(361\) −35100.9 −0.269342
\(362\) 329897.i 2.51745i
\(363\) −90388.8 18082.5i −0.685964 0.137229i
\(364\) −21574.5 −0.162831
\(365\) 171038.i 1.28383i
\(366\) −46698.2 + 233430.i −0.348609 + 1.74259i
\(367\) 204790. 1.52047 0.760233 0.649650i \(-0.225085\pi\)
0.760233 + 0.649650i \(0.225085\pi\)
\(368\) 80.5619i 0.000594887i
\(369\) −13282.5 + 31869.0i −0.0975501 + 0.234054i
\(370\) 194091. 1.41776
\(371\) 19858.0i 0.144274i
\(372\) 18436.9 + 3688.34i 0.133230 + 0.0266529i
\(373\) −37570.6 −0.270042 −0.135021 0.990843i \(-0.543110\pi\)
−0.135021 + 0.990843i \(0.543110\pi\)
\(374\) 141290.i 1.01011i
\(375\) 25237.8 126156.i 0.179469 0.897109i
\(376\) 36876.5 0.260840
\(377\) 3058.82i 0.0215215i
\(378\) 127908. 190072.i 0.895191 1.33026i
\(379\) 127620. 0.888465 0.444233 0.895911i \(-0.353476\pi\)
0.444233 + 0.895911i \(0.353476\pi\)
\(380\) 213977.i 1.48183i
\(381\) 212295. + 42470.0i 1.46248 + 0.292572i
\(382\) 236669. 1.62187
\(383\) 67921.4i 0.463030i −0.972831 0.231515i \(-0.925632\pi\)
0.972831 0.231515i \(-0.0743682\pi\)
\(384\) −46903.0 + 234454.i −0.318081 + 1.58999i
\(385\) 86118.5 0.580998
\(386\) 222812.i 1.49543i
\(387\) 77227.8 + 32187.4i 0.515646 + 0.214914i
\(388\) −398769. −2.64885
\(389\) 81552.6i 0.538938i 0.963009 + 0.269469i \(0.0868481\pi\)
−0.963009 + 0.269469i \(0.913152\pi\)
\(390\) 26210.9 + 5243.54i 0.172327 + 0.0344743i
\(391\) −22530.3 −0.147372
\(392\) 2892.81i 0.0188256i
\(393\) 34525.1 172580.i 0.223537 1.11739i
\(394\) −134834. −0.868572
\(395\) 69165.6i 0.443298i
\(396\) 53572.5 128538.i 0.341627 0.819672i
\(397\) −20135.3 −0.127754 −0.0638772 0.997958i \(-0.520347\pi\)
−0.0638772 + 0.997958i \(0.520347\pi\)
\(398\) 434808.i 2.74493i
\(399\) 132181. + 26443.2i 0.830280 + 0.166099i
\(400\) −106.626 −0.000666411
\(401\) 188063.i 1.16954i −0.811199 0.584770i \(-0.801185\pi\)
0.811199 0.584770i \(-0.198815\pi\)
\(402\) −91728.2 + 458521.i −0.567611 + 2.83731i
\(403\) −1381.99 −0.00850932
\(404\) 271580.i 1.66393i
\(405\) −124651. + 123562.i −0.759951 + 0.753315i
\(406\) −56060.8 −0.340100
\(407\) 74320.9i 0.448665i
\(408\) −186526. 37315.0i −1.12052 0.224162i
\(409\) 19089.1 0.114114 0.0570571 0.998371i \(-0.481828\pi\)
0.0570571 + 0.998371i \(0.481828\pi\)
\(410\) 73828.9i 0.439196i
\(411\) 18017.0 90061.3i 0.106659 0.533156i
\(412\) −58615.6 −0.345318
\(413\) 21997.0i 0.128962i
\(414\) −33148.4 13815.8i −0.193403 0.0806073i
\(415\) 100840. 0.585514
\(416\) 17493.5i 0.101086i
\(417\) 182563. + 36522.2i 1.04989 + 0.210032i
\(418\) 132510. 0.758397
\(419\) 152039.i 0.866018i 0.901390 + 0.433009i \(0.142548\pi\)
−0.901390 + 0.433009i \(0.857452\pi\)
\(420\) 59422.7 297036.i 0.336863 1.68388i
\(421\) 166921. 0.941776 0.470888 0.882193i \(-0.343934\pi\)
0.470888 + 0.882193i \(0.343934\pi\)
\(422\) 411987.i 2.31344i
\(423\) 17888.6 42920.4i 0.0999758 0.239874i
\(424\) −26281.0 −0.146187
\(425\) 29819.5i 0.165091i
\(426\) 544761. + 108981.i 3.00183 + 0.600524i
\(427\) −198291. −1.08754
\(428\) 547155.i 2.98692i
\(429\) −2007.84 + 10036.6i −0.0109098 + 0.0545346i
\(430\) 178909. 0.967597
\(431\) 1348.54i 0.00725954i −0.999993 0.00362977i \(-0.998845\pi\)
0.999993 0.00362977i \(-0.00115539\pi\)
\(432\) −711.550 478.835i −0.00381275 0.00256577i
\(433\) 293401. 1.56490 0.782449 0.622715i \(-0.213970\pi\)
0.782449 + 0.622715i \(0.213970\pi\)
\(434\) 25328.5i 0.134472i
\(435\) 42113.6 + 8424.92i 0.222558 + 0.0445233i
\(436\) −135787. −0.714307
\(437\) 21130.3i 0.110648i
\(438\) −73085.5 + 365332.i −0.380963 + 1.90432i
\(439\) −258719. −1.34245 −0.671227 0.741252i \(-0.734233\pi\)
−0.671227 + 0.741252i \(0.734233\pi\)
\(440\) 113973.i 0.588704i
\(441\) −3366.93 1403.29i −0.0173124 0.00721554i
\(442\) 36529.4 0.186981
\(443\) 89500.4i 0.456056i −0.973655 0.228028i \(-0.926772\pi\)
0.973655 0.228028i \(-0.0732277\pi\)
\(444\) 256344. + 51282.3i 1.30034 + 0.260136i
\(445\) −159630. −0.806112
\(446\) 391148.i 1.96640i
\(447\) 54489.0 272374.i 0.272705 1.36317i
\(448\) −321528. −1.60200
\(449\) 14364.7i 0.0712532i −0.999365 0.0356266i \(-0.988657\pi\)
0.999365 0.0356266i \(-0.0113427\pi\)
\(450\) −18285.5 + 43872.8i −0.0902988 + 0.216656i
\(451\) −28270.4 −0.138988
\(452\) 275584.i 1.34889i
\(453\) −185066. 37022.8i −0.901839 0.180415i
\(454\) −294754. −1.43004
\(455\) 22265.2i 0.107548i
\(456\) 34996.1 174935.i 0.168302 0.841292i
\(457\) −223969. −1.07240 −0.536198 0.844092i \(-0.680140\pi\)
−0.536198 + 0.844092i \(0.680140\pi\)
\(458\) 123371.i 0.588140i
\(459\) −133913. + 198996.i −0.635621 + 0.944535i
\(460\) −47483.6 −0.224403
\(461\) 293479.i 1.38094i −0.723361 0.690470i \(-0.757404\pi\)
0.723361 0.690470i \(-0.242596\pi\)
\(462\) 183946. + 36798.9i 0.861802 + 0.172405i
\(463\) −197511. −0.921361 −0.460680 0.887566i \(-0.652395\pi\)
−0.460680 + 0.887566i \(0.652395\pi\)
\(464\) 209.868i 0.000974788i
\(465\) 3806.42 19027.1i 0.0176040 0.0879969i
\(466\) −548403. −2.52539
\(467\) 368870.i 1.69137i −0.533680 0.845686i \(-0.679191\pi\)
0.533680 0.845686i \(-0.320809\pi\)
\(468\) 33232.3 + 13850.7i 0.151729 + 0.0632384i
\(469\) −389497. −1.77076
\(470\) 99430.9i 0.450117i
\(471\) −343912. 68800.4i −1.55026 0.310134i
\(472\) 29111.8 0.130673
\(473\) 68507.3i 0.306206i
\(474\) 29554.8 147736.i 0.131544 0.657549i
\(475\) −27966.4 −0.123951
\(476\) 413971.i 1.82707i
\(477\) −12748.7 + 30588.3i −0.0560312 + 0.134437i
\(478\) −661329. −2.89442
\(479\) 329730.i 1.43710i −0.695475 0.718550i \(-0.744806\pi\)
0.695475 0.718550i \(-0.255194\pi\)
\(480\) 240850. + 48182.5i 1.04535 + 0.209125i
\(481\) −19215.0 −0.0830522
\(482\) 55405.5i 0.238484i
\(483\) 5868.00 29332.3i 0.0251534 0.125734i
\(484\) −265492. −1.13334
\(485\) 411535.i 1.74954i
\(486\) −319049. + 210662.i −1.35078 + 0.891893i
\(487\) −87884.6 −0.370557 −0.185279 0.982686i \(-0.559319\pi\)
−0.185279 + 0.982686i \(0.559319\pi\)
\(488\) 262427.i 1.10197i
\(489\) 256742. + 51361.7i 1.07369 + 0.214794i
\(490\) −7799.95 −0.0324862
\(491\) 18504.7i 0.0767570i −0.999263 0.0383785i \(-0.987781\pi\)
0.999263 0.0383785i \(-0.0122193\pi\)
\(492\) −19506.9 + 97508.8i −0.0805856 + 0.402822i
\(493\) 58692.7 0.241485
\(494\) 34259.4i 0.140387i
\(495\) −132653. 55287.6i −0.541385 0.225641i
\(496\) 94.8193 0.000385419
\(497\) 462755.i 1.87343i
\(498\) 215391. + 43089.6i 0.868500 + 0.173745i
\(499\) 171794. 0.689934 0.344967 0.938615i \(-0.387890\pi\)
0.344967 + 0.938615i \(0.387890\pi\)
\(500\) 370548.i 1.48219i
\(501\) 53131.9 265590.i 0.211680 1.05812i
\(502\) 282805. 1.12222
\(503\) 256618.i 1.01426i 0.861868 + 0.507132i \(0.169294\pi\)
−0.861868 + 0.507132i \(0.830706\pi\)
\(504\) 97161.0 233120.i 0.382499 0.917739i
\(505\) −280274. −1.09901
\(506\) 29405.3i 0.114848i
\(507\) 249460. + 49905.0i 0.970476 + 0.194146i
\(508\) 623556. 2.41629
\(509\) 482881.i 1.86382i −0.362688 0.931911i \(-0.618141\pi\)
0.362688 0.931911i \(-0.381859\pi\)
\(510\) −100613. + 502934.i −0.386825 + 1.93362i
\(511\) −310336. −1.18848
\(512\) 2409.45i 0.00919132i
\(513\) −186630. 125592.i −0.709162 0.477228i
\(514\) −318148. −1.20421
\(515\) 60492.2i 0.228079i
\(516\) 236292. + 47270.8i 0.887462 + 0.177539i
\(517\) 38073.8 0.142444
\(518\) 352165.i 1.31246i
\(519\) −55775.1 + 278803.i −0.207065 + 1.03505i
\(520\) 29466.8 0.108975
\(521\) 55186.5i 0.203309i −0.994820 0.101655i \(-0.967586\pi\)
0.994820 0.101655i \(-0.0324137\pi\)
\(522\) 86353.4 + 35990.8i 0.316912 + 0.132084i
\(523\) −20140.8 −0.0736330 −0.0368165 0.999322i \(-0.511722\pi\)
−0.0368165 + 0.999322i \(0.511722\pi\)
\(524\) 506907.i 1.84614i
\(525\) −38822.1 7766.45i −0.140851 0.0281776i
\(526\) 664184. 2.40059
\(527\) 26517.6i 0.0954802i
\(528\) 137.760 688.618i 0.000494144 0.00247008i
\(529\) 275152. 0.983244
\(530\) 70861.9i 0.252267i
\(531\) 14121.9 33883.1i 0.0500847 0.120169i
\(532\) 388246. 1.37178
\(533\) 7309.06i 0.0257281i
\(534\) −340965. 68210.9i −1.19572 0.239206i
\(535\) 564672. 1.97283
\(536\) 515479.i 1.79424i
\(537\) −12407.4 + 62020.9i −0.0430262 + 0.215075i
\(538\) 129381. 0.446997
\(539\) 2986.74i 0.0102806i
\(540\) −282228. + 419391.i −0.967858 + 1.43824i
\(541\) −169569. −0.579366 −0.289683 0.957123i \(-0.593550\pi\)
−0.289683 + 0.957123i \(0.593550\pi\)
\(542\) 5999.11i 0.0204215i
\(543\) −449658. 89955.0i −1.52504 0.305088i
\(544\) 335666. 1.13425
\(545\) 140134.i 0.471792i
\(546\) −9514.05 + 47557.8i −0.0319139 + 0.159528i
\(547\) −395041. −1.32029 −0.660143 0.751140i \(-0.729504\pi\)
−0.660143 + 0.751140i \(0.729504\pi\)
\(548\) 264530.i 0.880874i
\(549\) 305437. + 127302.i 1.01339 + 0.422366i
\(550\) −38918.7 −0.128657
\(551\) 55045.4i 0.181308i
\(552\) −38819.8 7765.98i −0.127402 0.0254870i
\(553\) 125496. 0.410374
\(554\) 828512.i 2.69948i
\(555\) 52924.0 264551.i 0.171817 0.858862i
\(556\) 536230. 1.73461
\(557\) 322463.i 1.03937i 0.854358 + 0.519684i \(0.173950\pi\)
−0.854358 + 0.519684i \(0.826050\pi\)
\(558\) 16260.8 39014.9i 0.0522244 0.125303i
\(559\) −17712.0 −0.0566818
\(560\) 1527.63i 0.00487127i
\(561\) −192582. 38526.5i −0.611914 0.122415i
\(562\) 503230. 1.59329
\(563\) 434134.i 1.36964i 0.728711 + 0.684821i \(0.240120\pi\)
−0.728711 + 0.684821i \(0.759880\pi\)
\(564\) 26271.4 131323.i 0.0825894 0.412839i
\(565\) −284407. −0.890929
\(566\) 92188.5i 0.287769i
\(567\) −224195. 226170.i −0.697366 0.703509i
\(568\) 612431. 1.89828
\(569\) 32540.0i 0.100506i 0.998737 + 0.0502531i \(0.0160028\pi\)
−0.998737 + 0.0502531i \(0.983997\pi\)
\(570\) −471680. 94360.8i −1.45177 0.290430i
\(571\) −42779.4 −0.131209 −0.0656043 0.997846i \(-0.520898\pi\)
−0.0656043 + 0.997846i \(0.520898\pi\)
\(572\) 29479.7i 0.0901014i
\(573\) 64534.1 322586.i 0.196553 0.982509i
\(574\) −133957. −0.406577
\(575\) 6206.02i 0.0187706i
\(576\) 495266. + 206419.i 1.49277 + 0.622165i
\(577\) 625011. 1.87731 0.938655 0.344858i \(-0.112073\pi\)
0.938655 + 0.344858i \(0.112073\pi\)
\(578\) 160155.i 0.479386i
\(579\) 303699. + 60755.6i 0.905912 + 0.181230i
\(580\) 123697. 0.367708
\(581\) 182967.i 0.542028i
\(582\) −175851. + 879027.i −0.519158 + 2.59511i
\(583\) −27134.3 −0.0798327
\(584\) 410713.i 1.20424i
\(585\) 14294.2 34296.3i 0.0417683 0.100216i
\(586\) 613147. 1.78554
\(587\) 161202.i 0.467838i 0.972256 + 0.233919i \(0.0751551\pi\)
−0.972256 + 0.233919i \(0.924845\pi\)
\(588\) −10301.7 2060.88i −0.0297958 0.00596071i
\(589\) 24869.8 0.0716871
\(590\) 78494.7i 0.225495i
\(591\) −36765.9 + 183782.i −0.105262 + 0.526171i
\(592\) 1318.36 0.00376175
\(593\) 57859.8i 0.164539i 0.996610 + 0.0822693i \(0.0262168\pi\)
−0.996610 + 0.0822693i \(0.973783\pi\)
\(594\) −259718. 174776.i −0.736086 0.495346i
\(595\) −427225. −1.20676
\(596\) 800022.i 2.25221i
\(597\) 592653. + 118562.i 1.66285 + 0.332656i
\(598\) 7602.50 0.0212595
\(599\) 290228.i 0.808882i 0.914564 + 0.404441i \(0.132534\pi\)
−0.914564 + 0.404441i \(0.867466\pi\)
\(600\) −10278.5 + 51378.9i −0.0285513 + 0.142719i
\(601\) −385928. −1.06846 −0.534229 0.845340i \(-0.679398\pi\)
−0.534229 + 0.845340i \(0.679398\pi\)
\(602\) 324617.i 0.895733i
\(603\) 599963. + 250056.i 1.65002 + 0.687704i
\(604\) −543579. −1.49001
\(605\) 273992.i 0.748560i
\(606\) −598657. 119763.i −1.63017 0.326119i
\(607\) 508784. 1.38088 0.690440 0.723389i \(-0.257417\pi\)
0.690440 + 0.723389i \(0.257417\pi\)
\(608\) 314807.i 0.851603i
\(609\) −15286.4 + 76412.2i −0.0412166 + 0.206029i
\(610\) 707587. 1.90160
\(611\) 9843.67i 0.0263678i
\(612\) −265768. + 637662.i −0.709577 + 1.70250i
\(613\) −293162. −0.780167 −0.390083 0.920780i \(-0.627554\pi\)
−0.390083 + 0.920780i \(0.627554\pi\)
\(614\) 768508.i 2.03850i
\(615\) 100631. + 20131.4i 0.266060 + 0.0532259i
\(616\) 206796. 0.544981
\(617\) 124210.i 0.326276i −0.986603 0.163138i \(-0.947838\pi\)
0.986603 0.163138i \(-0.0521615\pi\)
\(618\) −25848.6 + 129209.i −0.0676801 + 0.338312i
\(619\) 326503. 0.852131 0.426065 0.904692i \(-0.359899\pi\)
0.426065 + 0.904692i \(0.359899\pi\)
\(620\) 55886.9i 0.145387i
\(621\) −27870.0 + 41414.9i −0.0722693 + 0.107392i
\(622\) −72694.6 −0.187898
\(623\) 289638.i 0.746242i
\(624\) 178.036 + 35.6166i 0.000457235 + 9.14709e-5i
\(625\) −439055. −1.12398
\(626\) 278998.i 0.711955i
\(627\) 36132.4 180615.i 0.0919097 0.459428i
\(628\) −1.01015e6 −2.56133
\(629\) 368698.i 0.931901i
\(630\) −628567. 261977.i −1.58369 0.660058i
\(631\) −421608. −1.05889 −0.529445 0.848345i \(-0.677600\pi\)
−0.529445 + 0.848345i \(0.677600\pi\)
\(632\) 166087.i 0.415817i
\(633\) −561549. 112339.i −1.40146 0.280365i
\(634\) −222547. −0.553661
\(635\) 643519.i 1.59593i
\(636\) −18722.9 + 93590.2i −0.0462871 + 0.231375i
\(637\) 772.195 0.00190304
\(638\) 76602.3i 0.188192i
\(639\) 297086. 712806.i 0.727581 1.74570i
\(640\) 710689. 1.73508
\(641\) 135933.i 0.330834i −0.986224 0.165417i \(-0.947103\pi\)
0.986224 0.165417i \(-0.0528970\pi\)
\(642\) 1.20612e6 + 241288.i 2.92632 + 0.585416i
\(643\) −293832. −0.710686 −0.355343 0.934736i \(-0.615636\pi\)
−0.355343 + 0.934736i \(0.615636\pi\)
\(644\) 86155.6i 0.207736i
\(645\) 48784.1 243857.i 0.117262 0.586159i
\(646\) −657369. −1.57523
\(647\) 585214.i 1.39800i 0.715123 + 0.698999i \(0.246371\pi\)
−0.715123 + 0.698999i \(0.753629\pi\)
\(648\) −299324. + 296710.i −0.712840 + 0.706615i
\(649\) 30057.0 0.0713602
\(650\) 10062.1i 0.0238156i
\(651\) 34523.4 + 6906.48i 0.0814613 + 0.0162965i
\(652\) 754107. 1.77394
\(653\) 449055.i 1.05311i −0.850142 0.526554i \(-0.823484\pi\)
0.850142 0.526554i \(-0.176516\pi\)
\(654\) −59880.0 + 299322.i −0.140000 + 0.699815i
\(655\) −523135. −1.21936
\(656\) 501.480i 0.00116532i
\(657\) 478027. + 199235.i 1.10744 + 0.461566i
\(658\) 180410. 0.416687
\(659\) 394456.i 0.908297i −0.890926 0.454149i \(-0.849944\pi\)
0.890926 0.454149i \(-0.150056\pi\)
\(660\) −405874. 81196.1i −0.931759 0.186401i
\(661\) 61363.2 0.140445 0.0702223 0.997531i \(-0.477629\pi\)
0.0702223 + 0.997531i \(0.477629\pi\)
\(662\) 491335.i 1.12114i
\(663\) 9960.70 49790.5i 0.0226602 0.113271i
\(664\) 242147. 0.549217
\(665\) 400676.i 0.906045i
\(666\) 226088. 542458.i 0.509718 1.22298i
\(667\) 12215.1 0.0274565
\(668\) 780097.i 1.74822i
\(669\) −533144. 106657.i −1.19122 0.238307i
\(670\) 1.38990e6 3.09623
\(671\) 270947.i 0.601783i
\(672\) −87423.8 + 437005.i −0.193594 + 0.967715i
\(673\) 678204. 1.49737 0.748687 0.662924i \(-0.230685\pi\)
0.748687 + 0.662924i \(0.230685\pi\)
\(674\) 922639.i 2.03101i
\(675\) 54813.7 + 36886.7i 0.120304 + 0.0809584i
\(676\) 732719. 1.60341
\(677\) 84970.9i 0.185393i 0.995694 + 0.0926964i \(0.0295486\pi\)
−0.995694 + 0.0926964i \(0.970451\pi\)
\(678\) −607484. 121529.i −1.32153 0.264374i
\(679\) −746702. −1.61960
\(680\) 565408.i 1.22277i
\(681\) −80372.3 + 401757.i −0.173305 + 0.866301i
\(682\) 34609.3 0.0744087
\(683\) 368714.i 0.790403i 0.918594 + 0.395201i \(0.129325\pi\)
−0.918594 + 0.395201i \(0.870675\pi\)
\(684\) −598036. 249252.i −1.27825 0.532754i
\(685\) −272999. −0.581808
\(686\) 768714.i 1.63349i
\(687\) −168157. 33640.2i −0.356288 0.0712763i
\(688\) 1215.23 0.00256733
\(689\) 7015.33i 0.0147778i
\(690\) −20939.6 + 104670.i −0.0439815 + 0.219850i
\(691\) 431721. 0.904164 0.452082 0.891976i \(-0.350681\pi\)
0.452082 + 0.891976i \(0.350681\pi\)
\(692\) 818906.i 1.71010i
\(693\) 100316. 240689.i 0.208882 0.501176i
\(694\) −1.19594e6 −2.48307
\(695\) 553397.i 1.14569i
\(696\) 101127. + 20230.8i 0.208761 + 0.0417632i
\(697\) 140246. 0.288686
\(698\) 440889.i 0.904937i
\(699\) −149536. + 747486.i −0.306050 + 1.52985i
\(700\) −114029. −0.232713
\(701\) 165775.i 0.337351i 0.985672 + 0.168676i \(0.0539490\pi\)
−0.985672 + 0.168676i \(0.946051\pi\)
\(702\) 45186.9 67147.8i 0.0916934 0.136257i
\(703\) 345786. 0.699676
\(704\) 439340.i 0.886453i
\(705\) −135527. 27112.4i −0.272676 0.0545495i
\(706\) 13701.4 0.0274887
\(707\) 508538.i 1.01738i
\(708\) 20739.7 103671.i 0.0413747 0.206819i
\(709\) −156571. −0.311472 −0.155736 0.987799i \(-0.549775\pi\)
−0.155736 + 0.987799i \(0.549775\pi\)
\(710\) 1.65131e6i 3.27576i
\(711\) −193308. 80567.9i −0.382394 0.159376i
\(712\) −383320. −0.756139
\(713\) 5518.84i 0.0108560i
\(714\) −912539. 182555.i −1.79001 0.358095i
\(715\) 30423.5 0.0595110
\(716\) 182169.i 0.355344i
\(717\) −180329. + 901407.i −0.350773 + 1.75341i
\(718\) −663007. −1.28608
\(719\) 731807.i 1.41559i 0.706416 + 0.707797i \(0.250311\pi\)
−0.706416 + 0.707797i \(0.749689\pi\)
\(720\) −980.731 + 2353.09i −0.00189184 + 0.00453914i
\(721\) −109759. −0.211139
\(722\) 227267.i 0.435976i
\(723\) −75519.1 15107.8i −0.144471 0.0289017i
\(724\) −1.32074e6 −2.51966
\(725\) 16167.0i 0.0307577i
\(726\) −117078. + 585238.i −0.222128 + 1.11035i
\(727\) −131366. −0.248549 −0.124275 0.992248i \(-0.539660\pi\)
−0.124275 + 0.992248i \(0.539660\pi\)
\(728\) 53465.4i 0.100881i
\(729\) 200140. + 492315.i 0.376598 + 0.926377i
\(730\) 1.10741e6 2.07809
\(731\) 339857.i 0.636007i
\(732\) 934539. + 186957.i 1.74412 + 0.348914i
\(733\) 145629. 0.271044 0.135522 0.990774i \(-0.456729\pi\)
0.135522 + 0.990774i \(0.456729\pi\)
\(734\) 1.32595e6i 2.46113i
\(735\) −2126.86 + 10631.5i −0.00393699 + 0.0196798i
\(736\) 69858.7 0.128963
\(737\) 532215.i 0.979834i
\(738\) 206342. + 86000.0i 0.378856 + 0.157901i
\(739\) 711310. 1.30248 0.651238 0.758873i \(-0.274250\pi\)
0.651238 + 0.758873i \(0.274250\pi\)
\(740\) 777045.i 1.41900i
\(741\) 46696.4 + 9341.72i 0.0850446 + 0.0170134i
\(742\) −128574. −0.233531
\(743\) 356613.i 0.645981i 0.946402 + 0.322991i \(0.104688\pi\)
−0.946402 + 0.322991i \(0.895312\pi\)
\(744\) 9140.36 45689.8i 0.0165127 0.0825418i
\(745\) −825635. −1.48756
\(746\) 243258.i 0.437108i
\(747\) 117464. 281834.i 0.210506 0.505071i
\(748\) −565657. −1.01100
\(749\) 1.02456e6i 1.82630i
\(750\) −816819. 163406.i −1.45212 0.290500i
\(751\) −747008. −1.32448 −0.662240 0.749292i \(-0.730394\pi\)
−0.662240 + 0.749292i \(0.730394\pi\)
\(752\) 675.381i 0.00119430i
\(753\) 77114.1 385470.i 0.136002 0.679830i
\(754\) −19804.9 −0.0348361
\(755\) 560981.i 0.984135i
\(756\) −760955. 512082.i −1.33142 0.895975i
\(757\) −376457. −0.656937 −0.328469 0.944515i \(-0.606533\pi\)
−0.328469 + 0.944515i \(0.606533\pi\)
\(758\) 826298.i 1.43813i
\(759\) −40080.2 8018.13i −0.0695738 0.0139184i
\(760\) −530273. −0.918062
\(761\) 1.05381e6i 1.81968i 0.414965 + 0.909838i \(0.363794\pi\)
−0.414965 + 0.909838i \(0.636206\pi\)
\(762\) 274979. 1.37454e6i 0.473577 2.36726i
\(763\) −254263. −0.436752
\(764\) 947508.i 1.62329i
\(765\) 658076. + 274276.i 1.12448 + 0.468668i
\(766\) −439769. −0.749492
\(767\) 7770.98i 0.0132095i
\(768\) 582658. + 116562.i 0.987851 + 0.197622i
\(769\) 321414. 0.543515 0.271758 0.962366i \(-0.412395\pi\)
0.271758 + 0.962366i \(0.412395\pi\)
\(770\) 557589.i 0.940443i
\(771\) −86751.2 + 433643.i −0.145938 + 0.729497i
\(772\) 892031. 1.49674
\(773\) 618982.i 1.03590i 0.855410 + 0.517951i \(0.173305\pi\)
−0.855410 + 0.517951i \(0.826695\pi\)
\(774\) 208403. 500025.i 0.347874 0.834661i
\(775\) −7304.33 −0.0121612
\(776\) 988219.i 1.64108i
\(777\) 480009. + 96027.0i 0.795074 + 0.159056i
\(778\) 528026. 0.872361
\(779\) 131531.i 0.216747i
\(780\) 20992.6 104935.i 0.0345045 0.172478i
\(781\) 632315. 1.03665
\(782\) 145877.i